{nlstimedist}
{nlstimedist} fits a biologically meaningful distribution function to time-sequence data (phenology), estimates parameters to draw the cumulative distribution function and probability density function and calculates standard statistical moments and percentiles.
Installation
You can install:
- the latest released version from CRAN with
install.packages("nlstimedist")- the latest development version from GitHub with
# install.packages("remotes")
remotes::install_github("nathaneastwood/nlstimedist")Usage
Preparing the data
Data should be in tidy format. {nlstimedist} provides three example tidy
datasets: lobelia, pupae and tilia.
library(nlstimedist)
head(tilia)
# Day Trees
# 1 94 0
# 2 95 0
# 3 96 1
# 4 103 1
# 5 104 0
# 6 105 3We first need to calculate the cumulative number of trees as well as the
proportions. We do this using the tdData() function.
tdTilia <- tdData(tilia, x = "Day", y = "Trees")
tdTilia
# Day Trees cumN propMax
# 3 96 1 1 0.01538462
# 4 103 1 2 0.03076923
# 6 105 3 5 0.07692308
# 8 107 1 6 0.09230769
# 10 110 4 10 0.15384615
# 11 111 7 17 0.26153846
# 12 112 3 20 0.30769231
# 14 114 1 21 0.32307692
# 15 115 3 24 0.36923077
# 16 116 6 30 0.46153846
# 18 117 3 33 0.50769231
# 19 118 2 35 0.53846154
# 20 119 2 37 0.56923077
# 21 120 5 42 0.64615385
# 22 121 2 44 0.67692308
# 23 122 2 46 0.70769231
# 24 123 4 50 0.76923077
# 25 124 1 51 0.78461538
# 27 126 3 54 0.83076923
# 28 127 1 55 0.84615385
# 29 128 1 56 0.86153846
# 30 129 1 57 0.87692308
# 31 130 2 59 0.90769231
# 32 131 4 63 0.96923077
# 33 133 1 64 0.98461538
# 34 134 1 65 1.00000000Fitting the model
We fit the model to the proportion of the cumulative number of trees
(propMax) in the tdTilia object using the timedist() function.
model <- timedist(data = tdTilia, x = "Day", y = "propMax", r = 0.1, c = 0.5, t = 120)
model
# Nonlinear regression model
# model: propMax ~ 1 - (1 - (r/(1 + exp(-c * (Day - t)))))^Day
# data: data
# r c t
# 0.02721 0.17126 124.84320
# residual sum-of-squares: 0.01806
#
# Number of iterations to convergence: 10
# Achieved convergence tolerance: 1.49e-08Extracting the moments
We can extract the mean, variance, standard deviation, skew, kurtosis and entropy of the model as follows.
model$m$getMoments()
# mean variance sd skew kurtosis entropy
# 1 118.0325 180.7509 13.44436 4.324762 46.82073 5.36145Extracting the RSS
Similarly we can extract the RSS of the model
model$m$rss()
# [1] 0.9930469Plotting the PDF and CDF
The probability density function (PDF) and the cumulative distribution function (CDF) of the model have their own plotting functions.
tdPdfPlot(model)
tdCdfPlot(model)
